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Stochastic Viability and Comparison Theorems for Mixed Stochastic Differential Equations

Author

Listed:
  • Alexander Melnikov

    (University of Alberta)

  • Yuliya Mishura

    (Kyiv National Taras Shevchenko University)

  • Georgiy Shevchenko

    (Kyiv National Taras Shevchenko University)

Abstract

For a mixed stochastic differential equation containing both Wiener process and a Hölder continuous process with exponent γ > 1/2, we prove a stochastic viability theorem. As a consequence, we get a result about positivity of solution and a pathwise comparison theorem. An application to option price estimation is given.

Suggested Citation

  • Alexander Melnikov & Yuliya Mishura & Georgiy Shevchenko, 2015. "Stochastic Viability and Comparison Theorems for Mixed Stochastic Differential Equations," Methodology and Computing in Applied Probability, Springer, vol. 17(1), pages 169-188, March.
    • Handle: RePEc:spr:metcap:v:17:y:2015:i:1:d:10.1007_s11009-013-9336-9
    DOI: 10.1007/s11009-013-9336-9
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    References listed on IDEAS

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    1. Hu, Yaozhong & Nualart, David & Song, Xiaoming, 2008. "A singular stochastic differential equation driven by fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2075-2085, October.
    2. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    3. Kubilius, K., 2002. "The existence and uniqueness of the solution of an integral equation driven by a p-semimartingale of special type," Stochastic Processes and their Applications, Elsevier, vol. 98(2), pages 289-315, April.
    4. Christian Bender & Tommi Sottinen & Esko Valkeila, 2010. "Fractional processes as models in stochastic finance," Papers 1004.3106, arXiv.org.
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    Cited by:

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    2. Coutin, Laure & Marie, Nicolas, 2017. "Invariance for rough differential equations," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2373-2395.

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